Subgroups — C₇₉×#24445 #34136134

Order 20224.

1454 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#468×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#448×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#448×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#419×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2414	C₂	1	1	yes	maximal, characteristic
7	C₇₉×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2013	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1870	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
22	D₄×Q₈×C₇₉	—	2	4	no	—
23	D₄×Q₈×C₇₉	—	2	4	no	—
24	C₂×C₄⋊Q₈×C₇₉	—	2	1	no	—
25	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
28	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₇₉	—	2	1	no	—
34	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
36	#468×C₇₉	—	2	4	no	—
37	#448×C₇₉	—	2	4	no	—
38	#448×C₇₉	—	2	4	no	—
39	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
40	#419×C₇₉	—	2	4	no	—
41	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
44	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
48	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
49	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
50	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
54	#394×C₇₉	—	2	1	no	—
55	#392×C₇₉	—	2	1	no	—
56	#390×C₇₉	—	2	1	no	—
57	#390×C₇₉	C₂²	1	1	yes	characteristic
58	#389×C₇₉	C₂²	1	1	yes	characteristic
59	#388×C₇₉	—	2	1	no	—
60	#380×C₇₉	C₂²	1	1	yes	characteristic
61	#340×C₇₉	C₂²	1	1	yes	characteristic
62	#340×C₇₉	C₂²	1	1	yes	characteristic
63	#336×C₇₉	C₂²	1	1	yes	characteristic
64	#336×C₇₉	C₂²	1	1	yes	characteristic
65	C₂²×Q₈×C₇₉	—	2	2	no	—
66	C₂²×Q₈×C₇₉	—	2	2	no	—
67	C₂²×Q₈×C₇₉	—	2	1	no	—
68	C₂²×Q₈×C₇₉	—	2	1	no	—
69	C₂²×Q₈×C₇₉	—	2	2	no	—
70	C₂²×Q₈×C₇₉	—	2	2	no	—
71	C₂²×Q₈×C₇₉	—	2	2	no	—
72	C₂²×Q₈×C₇₉	—	2	2	no	—
73	C₂²×Q₈×C₇₉	—	2	2	no	—
74	C₂²×Q₈×C₇₉	—	4	1	no	—
75	C₂²×Q₈×C₇₉	—	4	1	no	—
76	C₂²×Q₈×C₇₉	—	4	1	no	—
77	C₂²×Q₈×C₇₉	—	4	1	no	—
78	C₂²×Q₈×C₇₉	D₄	1	4	yes	complemented
79	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₇₉	—	2	1	no	—
83	C₂²×D₄×C₇₉	—	2	1	no	—
84	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
85	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₇₉	—	2	1	no	—
87	C₂³×C₄×C₇₉	—	2	1	no	—
88	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
90	C₂×SD₁₆×C₇₉	—	2	2	no	—
91	C₂×SD₁₆×C₇₉	—	2	2	no	—
92	C₂×SD₁₆×C₇₉	—	2	2	no	—
93	C₂×SD₁₆×C₇₉	—	2	2	no	—
94	C₂×SD₁₆×C₇₉	—	2	2	no	—
95	C₂×SD₁₆×C₇₉	—	2	2	no	—
96	C₂×SD₁₆×C₇₉	—	4	1	no	—
97	C₂×SD₁₆×C₇₉	—	4	1	no	—
98	C₂×SD₁₆×C₇₉	—	4	1	no	—
99	C₂×M₁₆×C₇₉	—	2	2	no	—
100	C₂×M₁₆×C₇₉	—	2	2	no	—
101	C₂×M₁₆×C₇₉	—	4	1	no	—
102	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
106	C₄⋊Q₈×C₇₉	—	2	8	no	—
107	C₄⋊Q₈×C₇₉	—	2	2	no	—
108	C₄⋊Q₈×C₇₉	—	2	2	no	—
109	C₂²⋊Q₈×C₇₉	—	2	8	no	—
110	C₂²⋊Q₈×C₇₉	—	2	8	no	—
111	C₂²⋊Q₈×C₇₉	—	2	2	no	—
112	C₂²⋊Q₈×C₇₉	—	2	2	no	—
113	C₂²⋊Q₈×C₇₉	—	2	2	no	—
114	C₂²⋊Q₈×C₇₉	D₄	1	4	yes	complemented
115	#121×C₇₉	—	2	2	no	—
116	#121×C₇₉	—	2	2	no	—
117	#121×C₇₉	—	2	2	no	—
118	#121×C₇₉	—	4	1	no	—
119	C₄×Q₈×C₇₉	—	2	2	no	—
120	C₄×Q₈×C₇₉	—	2	2	no	—
121	C₄×D₄×C₇₉	—	2	8	no	—
122	C₄×D₄×C₇₉	—	2	2	no	—
123	C₄×D₄×C₇₉	—	2	2	no	—
124	#117×C₇₉	—	2	2	no	—
125	#117×C₇₉	—	4	1	no	—
126	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
127	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
129	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
130	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
131	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
132	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
138	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
140	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
147	C₂×C₄²×C₇₉	—	2	1	no	—
148	C₂×C₄²×C₇₉	—	2	1	no	—
149	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
150	#107×C₇₉	—	2	2	no	—
151	#103×C₇₉	—	2	2	no	—
152	#103×C₇₉	—	2	2	no	—
153	#103×C₇₉	—	2	2	no	—
154	#103×C₇₉	—	2	2	no	—
155	#103×C₇₉	—	2	2	no	—
156	#103×C₇₉	—	2	2	no	—
157	#103×C₇₉	—	2	2	no	—
158	#103×C₇₉	—	4	1	no	—
159	#103×C₇₉	D₄	1	4	yes	complemented
160	#102×C₇₉	—	2	2	no	—
161	C₂²⋊C₈×C₇₉	—	2	2	no	—
162	C₂²⋊C₈×C₇₉	—	2	2	no	—
163	C₂²⋊C₈×C₇₉	—	4	1	no	—
164	#95×C₇₉	—	2	1	no	—
165	#95×C₇₉	—	2	1	no	—
166	C₂⁴×C₇₉	—	2	1	no	—
167	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
168	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
169	C₂×Q₈×C₇₉	—	2	4	no	—
170	C₂×Q₈×C₇₉	—	2	4	no	—
171	C₂×Q₈×C₇₉	—	2	1	no	—
172	C₂×Q₈×C₇₉	—	2	1	no	—
173	C₂×Q₈×C₇₉	—	2	1	no	—
174	C₂×Q₈×C₇₉	—	2	1	no	—
175	C₂×Q₈×C₇₉	—	2	1	no	—
176	C₂×Q₈×C₇₉	—	2	8	no	—
177	C₂×Q₈×C₇₉	—	2	1	no	—
178	C₂×Q₈×C₇₉	—	2	1	no	—
179	C₂×Q₈×C₇₉	—	2	1	no	—
180	C₂×Q₈×C₇₉	—	2	1	no	—
181	C₂×Q₈×C₇₉	—	2	1	no	—
182	C₂×Q₈×C₇₉	—	2	1	no	—
183	C₂×Q₈×C₇₉	—	2	1	no	—
184	C₂×Q₈×C₇₉	—	2	1	no	—
185	C₂×Q₈×C₇₉	—	4	2	no	—
186	C₂×Q₈×C₇₉	—	4	2	no	—
187	C₂×Q₈×C₇₉	—	4	2	no	—
188	C₂×Q₈×C₇₉	—	4	2	no	—
189	C₂×Q₈×C₇₉	—	4	4	no	—
190	C₂×Q₈×C₇₉	—	4	4	no	—
191	C₂×Q₈×C₇₉	—	4	4	no	—
192	C₂×Q₈×C₇₉	—	4	4	no	—
193	C₂×Q₈×C₇₉	—	4	4	no	—
194	C₂×Q₈×C₇₉	—	4	4	no	—
195	C₂×Q₈×C₇₉	—	4	4	no	—
196	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
197	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
198	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
199	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
200	C₂×Q₈×C₇₉	#41	1	2	yes	—
201	C₂×D₄×C₇₉	—	2	2	no	—
202	C₂×D₄×C₇₉	—	2	2	no	—
203	C₂×D₄×C₇₉	—	2	2	no	—
204	C₂×D₄×C₇₉	—	2	1	no	—
205	C₂×D₄×C₇₉	—	2	1	no	—
206	C₂×D₄×C₇₉	—	2	1	no	—
207	C₂×D₄×C₇₉	—	2	1	no	—
208	C₂×D₄×C₇₉	—	2	1	no	—
209	C₂×D₄×C₇₉	—	2	1	no	—
210	C₂×D₄×C₇₉	—	4	2	no	—
211	C₂×D₄×C₇₉	—	4	2	no	—
212	C₂×D₄×C₇₉	—	4	2	no	—
213	C₂×D₄×C₇₉	—	8	1	no	—
214	C₂×D₄×C₇₉	—	8	1	no	—
215	C₂×D₄×C₇₉	—	8	1	no	—
216	C₂²×C₄×C₇₉	—	2	1	no	—
217	C₂²×C₄×C₇₉	—	2	1	no	—
218	C₂²×C₄×C₇₉	—	2	1	no	—
219	C₂²×C₄×C₇₉	—	2	1	no	—
220	C₂²×C₄×C₇₉	—	2	1	no	—
221	C₂²×C₄×C₇₉	—	2	4	no	—
222	C₂²×C₄×C₇₉	—	2	4	no	—
223	C₂²×C₄×C₇₉	—	2	1	no	—
224	C₂²×C₄×C₇₉	—	2	1	no	—
225	C₂²×C₄×C₇₉	—	2	1	no	—
226	C₂²×C₄×C₇₉	—	2	1	no	—
227	C₂²×C₄×C₇₉	—	2	1	no	—
228	C₂²×C₄×C₇₉	—	2	1	no	—
229	C₂²×C₄×C₇₉	—	2	1	no	—
230	C₂²×C₄×C₇₉	—	2	1	no	—
231	C₂²×C₄×C₇₉	—	2	1	no	—
232	C₂²×C₄×C₇₉	—	2	1	no	—
233	C₂²×C₄×C₇₉	—	2	1	no	—
234	C₂²×C₄×C₇₉	—	2	1	no	—
235	C₂²×C₄×C₇₉	—	4	2	no	—
236	C₂²×C₄×C₇₉	—	4	2	no	—
237	C₂²×C₄×C₇₉	—	4	2	no	—
238	C₂²×C₄×C₇₉	—	4	2	no	—
239	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
243	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
244	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
246	SD₁₆×C₇₉	—	4	4	no	—
247	SD₁₆×C₇₉	—	4	4	no	—
248	SD₁₆×C₇₉	—	4	4	no	—
249	M₁₆×C₇₉	—	4	4	no	—
250	C₂×C₈×C₇₉	—	2	1	no	—
251	C₂×C₈×C₇₉	—	2	1	no	—
252	C₂×C₈×C₇₉	—	2	1	no	—
253	C₂×C₈×C₇₉	—	2	1	no	—
254	C₂×C₈×C₇₉	—	2	1	no	—
255	C₂×C₈×C₇₉	—	2	1	no	—
256	C₂×C₈×C₇₉	—	2	1	no	—
257	C₂×C₈×C₇₉	—	2	1	no	—
258	C₂×C₈×C₇₉	—	2	1	no	—
259	C₂×C₈×C₇₉	—	2	1	no	—
260	C₂×C₈×C₇₉	—	2	1	no	—
261	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₇₉	—	2	4	no	—
263	C₄⋊C₄×C₇₉	—	2	4	no	—
264	C₄⋊C₄×C₇₉	—	2	4	no	—
265	C₄⋊C₄×C₇₉	—	2	4	no	—
266	C₄⋊C₄×C₇₉	—	2	4	no	—
267	C₄⋊C₄×C₇₉	—	2	2	no	—
268	C₄⋊C₄×C₇₉	—	2	1	no	—
269	C₄⋊C₄×C₇₉	—	2	1	no	—
270	C₄⋊C₄×C₇₉	—	2	1	no	—
271	C₄⋊C₄×C₇₉	—	2	1	no	—
272	C₄⋊C₄×C₇₉	—	2	1	no	—
273	C₄⋊C₄×C₇₉	—	2	1	no	—
274	C₄⋊C₄×C₇₉	—	8	1	no	—
275	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₇₉	—	2	4	no	—
278	C₂²⋊C₄×C₇₉	—	2	4	no	—
279	C₂²⋊C₄×C₇₉	—	2	2	no	—
280	C₂²⋊C₄×C₇₉	—	2	2	no	—
281	C₂²⋊C₄×C₇₉	—	4	2	no	—
282	C₂²⋊C₄×C₇₉	—	4	2	no	—
283	C₂²⋊C₄×C₇₉	—	4	2	no	—
284	C₂²⋊C₄×C₇₉	—	4	2	no	—
285	C₂²⋊C₄×C₇₉	—	8	1	no	—
286	C₂²⋊C₄×C₇₉	—	8	1	no	—
287	C₄²×C₇₉	—	2	4	no	—
288	C₄²×C₇₉	—	2	1	no	—
289	C₄²×C₇₉	—	2	1	no	—
290	C₄²×C₇₉	—	4	2	no	—
291	C₂³×C₇₉	—	2	1	no	—
292	C₂³×C₇₉	—	2	1	no	—
293	C₂³×C₇₉	—	2	1	no	—
294	C₂³×C₇₉	—	2	1	no	—
295	C₂³×C₇₉	—	2	1	no	—
296	C₂³×C₇₉	—	2	1	no	—
297	C₂³×C₇₉	—	2	1	no	—
298	C₂³×C₇₉	—	2	1	no	—
299	C₂³×C₇₉	—	2	1	no	—
300	C₂³×C₇₉	—	2	1	no	—
301	C₂³×C₇₉	—	2	1	no	—
302	C₂³×C₇₉	—	2	1	no	—
303	C₂³×C₇₉	—	4	1	no	—
304	C₂³×C₇₉	—	4	1	no	—
305	C₂³×C₇₉	—	4	1	no	—
306	C₂³×C₇₉	—	4	1	no	—
307	C₂³×C₇₉	—	4	1	no	—
308	C₂³×C₇₉	—	4	1	no	—
309	C₂³×C₇₉	—	4	1	no	—
310	C₂³×C₇₉	#120	1	2	yes	—
311	C₂³×C₇₉	#137	1	2	yes	—
312	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
313	Q₈×C₇₉	—	2	2	no	—
314	Q₈×C₇₉	—	2	2	no	—
315	Q₈×C₇₉	—	2	2	no	—
316	Q₈×C₇₉	—	2	2	no	—
317	Q₈×C₇₉	—	2	2	no	—
318	Q₈×C₇₉	—	2	2	no	—
319	Q₈×C₇₉	—	2	2	no	—
320	Q₈×C₇₉	—	4	8	no	—
321	Q₈×C₇₉	—	4	8	no	—
322	Q₈×C₇₉	—	4	1	no	—
323	Q₈×C₇₉	—	4	1	no	—
324	Q₈×C₇₉	—	4	1	no	—
325	Q₈×C₇₉	—	4	1	no	—
326	Q₈×C₇₉	#121	1	4	yes	—
327	D₄×C₇₉	—	2	8	no	—
328	D₄×C₇₉	—	4	1	no	—
329	D₄×C₇₉	—	4	1	no	—
330	D₄×C₇₉	—	4	1	no	—
331	D₄×C₇₉	—	4	1	no	—
332	D₄×C₇₉	—	8	4	no	—
333	D₄×C₇₉	—	8	4	no	—
334	C₂×C₄×C₇₉	—	2	1	no	—
335	C₂×C₄×C₇₉	—	2	2	no	—
336	C₂×C₄×C₇₉	—	2	1	no	—
337	C₂×C₄×C₇₉	—	2	2	no	—
338	C₂×C₄×C₇₉	—	2	1	no	—
339	C₂×C₄×C₇₉	—	2	2	no	—
340	C₂×C₄×C₇₉	—	2	1	no	—
341	C₂×C₄×C₇₉	—	2	2	no	—
342	C₂×C₄×C₇₉	—	2	2	no	—
343	C₂×C₄×C₇₉	—	2	2	no	—
344	C₂×C₄×C₇₉	—	2	2	no	—
345	C₂×C₄×C₇₉	—	2	1	no	—
346	C₂×C₄×C₇₉	—	2	2	no	—
347	C₂×C₄×C₇₉	—	2	2	no	—
348	C₂×C₄×C₇₉	—	2	2	no	—
349	C₂×C₄×C₇₉	—	2	1	no	—
350	C₂×C₄×C₇₉	—	2	2	no	—
351	C₂×C₄×C₇₉	—	2	1	no	—
352	C₂×C₄×C₇₉	—	2	1	no	—
353	C₂×C₄×C₇₉	—	2	1	no	—
354	C₂×C₄×C₇₉	—	2	1	no	—
355	C₂×C₄×C₇₉	—	4	8	no	—
356	C₂×C₄×C₇₉	—	4	8	no	—
357	C₂×C₄×C₇₉	—	4	1	no	—
358	C₂×C₄×C₇₉	—	4	1	no	—
359	C₂×C₄×C₇₉	—	4	1	no	—
360	C₂×C₄×C₇₉	—	4	1	no	—
361	C₂×C₄×C₇₉	—	4	1	no	—
362	C₂×C₄×C₇₉	—	4	1	no	—
363	C₂×C₄×C₇₉	—	4	1	no	—
364	C₂×C₄×C₇₉	—	4	1	no	—
365	C₂×C₄×C₇₉	—	4	1	no	—
366	C₂×C₄×C₇₉	—	4	1	no	—
367	C₂×C₄×C₇₉	—	4	1	no	—
368	C₂×C₄×C₇₉	—	4	1	no	—
369	C₂×C₄×C₇₉	—	4	1	no	—
370	C₂×C₄×C₇₉	—	4	1	no	—
371	C₂×C₄×C₇₉	—	4	1	no	—
372	C₂×C₄×C₇₉	—	4	1	no	—
373	C₂×C₄×C₇₉	—	4	1	no	—
374	C₂×C₄×C₇₉	—	4	1	no	—
375	C₂×C₄×C₇₉	#120	1	2	yes	—
376	C₂×C₄×C₇₉	#137	1	2	yes	—
377	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
381	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
383	C₈×C₇₉	—	2	2	no	—
384	C₈×C₇₉	—	4	1	no	—
385	C₈×C₇₉	—	4	1	no	—
386	C₈×C₇₉	—	4	1	no	—
387	C₂²×C₇₉	—	2	2	no	—
388	C₂²×C₇₉	—	2	2	no	—
389	C₂²×C₇₉	—	2	2	no	—
390	C₂²×C₇₉	—	2	2	no	—
391	C₂²×C₇₉	—	2	2	no	—
392	C₂²×C₇₉	—	2	2	no	—
393	C₂²×C₇₉	—	4	1	no	—
394	C₂²×C₇₉	—	4	1	no	—
395	C₂²×C₇₉	—	4	1	no	—
396	C₂²×C₇₉	—	4	1	no	—
397	C₂²×C₇₉	—	4	1	no	—
398	C₂²×C₇₉	—	4	1	no	—
399	C₂²×C₇₉	—	4	1	no	—
400	C₂²×C₇₉	—	4	1	no	—
401	C₂²×C₇₉	—	8	1	no	—
402	C₂²×C₇₉	—	8	1	no	—
403	C₂²×C₇₉	—	8	1	no	—
404	C₂²×C₇₉	—	8	1	no	—
405	C₂²×C₇₉	—	8	1	no	—
406	C₂²×C₇₉	—	8	1	no	—
407	C₂²×C₇₉	—	8	1	no	—
408	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
409	C₂²×C₇₉	D₄²	1	1	yes	characteristic
410	C₂²×C₇₉	#546	1	1	yes	characteristic
411	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
412	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
413	C₂²×C₇₉	#577	1	1	yes	characteristic
414	C₂²×C₇₉	#577	1	1	yes	characteristic
415	C₄×C₇₉	—	2	2	no	—
416	C₄×C₇₉	—	2	4	no	—
417	C₄×C₇₉	—	2	2	no	—
418	C₄×C₇₉	—	4	1	no	—
419	C₄×C₇₉	—	4	2	no	—
420	C₄×C₇₉	—	4	2	no	—
421	C₄×C₇₉	—	4	1	no	—
422	C₄×C₇₉	—	4	2	no	—
423	C₄×C₇₉	—	4	2	no	—
424	C₄×C₇₉	—	8	1	no	—
425	C₄×C₇₉	—	8	1	no	—
426	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
427	C₄×C₇₉	#534	1	1	yes	characteristic
428	C₄×C₇₉	D₄²	1	1	yes	characteristic
429	C₄×C₇₉	#546	1	1	yes	characteristic
430	#24445	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
431	C₂×C₇₉	—	4	2	no	—
432	C₂×C₇₉	—	4	2	no	—
433	C₂×C₇₉	—	16	1	no	—
434	C₂×C₇₉	#2410	1	1	yes	characteristic
435	C₂×C₇₉	#3004	1	1	yes	characteristic
436	C₂×C₇₉	#3010	1	1	yes	characteristic
437	C₂×C₇₉	#3266	1	1	yes	characteristic
438	C₂×C₇₉	#3278	1	1	yes	characteristic
439	C₂×C₇₉	#3320	1	1	yes	characteristic
440	C₂×C₇₉	#3329	1	1	yes	characteristic
441	C₂×D₄×Q₈	C₂×C₇₉	1	1	yes	characteristic, complemented
442	C₂×#468	C₂×C₇₉	1	1	yes	characteristic, complemented
443	C₂×#448	C₂×C₇₉	1	1	yes	characteristic, complemented
444	C₂×#448	C₂×C₇₉	1	1	yes	characteristic, complemented
445	C₂×#419	C₂×C₇₉	1	1	yes	characteristic, complemented
446	#2414	C₂×C₇₉	1	1	yes	characteristic
447	#2043	C₂×C₇₉	1	1	yes	characteristic, complemented
448	#2036	C₂×C₇₉	1	1	yes	characteristic, complemented
449	#2013	C₂×C₇₉	1	1	yes	characteristic, complemented
450	#2000	C₂×C₇₉	1	1	yes	characteristic, complemented
451	#1880	C₂×C₇₉	1	1	yes	characteristic, complemented
452	#1873	C₂×C₇₉	1	1	yes	characteristic, complemented
453	#1870	C₂×C₇₉	1	1	yes	characteristic, complemented
454	#1863	C₂×C₇₉	1	1	yes	characteristic, complemented
455	#1787	C₂×C₇₉	1	1	yes	characteristic, complemented
456	C₇₉	#24445	1	1	yes	characteristic, direct product factor, Sylow
457	C₂³×Q₈	C₂²×C₇₉	1	1	yes	characteristic
458	C₂³×Q₈	C₂²×C₇₉	1	1	yes	characteristic
459	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
460	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
461	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
462	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
463	D₄×Q₈	—	2	4	no	—
464	D₄×Q₈	—	2	4	no	—
465	C₂×C₄⋊Q₈	—	2	1	no	—
466	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
467	C₂×C₂²⋊Q₈	—	2	1	no	—
468	C₂×C₂²⋊Q₈	—	2	1	no	—
469	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
470	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
471	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
472	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
473	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
474	C₂×C₄×D₄	—	2	1	no	—
475	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
476	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
477	#468	—	2	4	no	—
478	#448	—	2	4	no	—
479	#448	—	2	4	no	—
480	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
481	#419	—	2	4	no	—
482	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
483	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
484	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
485	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
486	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
487	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
488	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
489	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
490	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
491	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
492	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
493	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
494	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
495	#394	—	2	1	no	—
496	#392	—	2	1	no	—
497	#390	—	2	1	no	—
498	#390	C₂²×C₇₉	1	1	yes	characteristic
499	#389	C₂²×C₇₉	1	1	yes	characteristic
500	#388	—	2	1	no	—
501	#380	C₂²×C₇₉	1	1	yes	characteristic
502	#340	C₂²×C₇₉	1	1	yes	characteristic
503	#340	C₂²×C₇₉	1	1	yes	characteristic
504	#336	C₂²×C₇₉	1	1	yes	characteristic
505	#336	C₂²×C₇₉	1	1	yes	characteristic
506	C₂²×Q₈	—	2	2	no	—
507	C₂²×Q₈	—	2	2	no	—
508	C₂²×Q₈	—	2	1	no	—
509	C₂²×Q₈	—	2	1	no	—
510	C₂²×Q₈	—	2	2	no	—
511	C₂²×Q₈	—	2	2	no	—
512	C₂²×Q₈	—	2	2	no	—
513	C₂²×Q₈	—	2	2	no	—
514	C₂²×Q₈	—	2	2	no	—
515	C₂²×Q₈	—	4	1	no	—
516	C₂²×Q₈	—	4	1	no	—
517	C₂²×Q₈	—	4	1	no	—
518	C₂²×Q₈	—	4	1	no	—
519	C₂²×Q₈	D₄×C₇₉	1	4	yes	complemented
520	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
521	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
522	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
526	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
527	C₂³×C₄	—	2	1	no	—
528	C₂³×C₄	—	2	1	no	—
529	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
531	C₂×SD₁₆	—	2	2	no	—
532	C₂×SD₁₆	—	2	2	no	—
533	C₂×SD₁₆	—	2	2	no	—
534	C₂×SD₁₆	—	2	2	no	—
535	C₂×SD₁₆	—	2	2	no	—
536	C₂×SD₁₆	—	2	2	no	—
537	C₂×SD₁₆	—	4	1	no	—
538	C₂×SD₁₆	—	4	1	no	—
539	C₂×SD₁₆	—	4	1	no	—
540	C₂×M₁₆	—	2	2	no	—
541	C₂×M₁₆	—	2	2	no	—
542	C₂×M₁₆	—	4	1	no	—
543	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
544	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
545	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
546	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
547	C₄⋊Q₈	—	2	8	no	—
548	C₄⋊Q₈	—	2	2	no	—
549	C₄⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	8	no	—
551	C₂²⋊Q₈	—	2	8	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	D₄×C₇₉	1	4	yes	complemented
556	#121	—	2	2	no	—
557	#121	—	2	2	no	—
558	#121	—	2	2	no	—
559	#121	—	4	1	no	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×D₄	—	2	8	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	#117	—	2	2	no	—
566	#117	—	4	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	1	no	—
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₂²⋊C₄	—	2	1	no	—
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
587	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
588	C₂×C₄²	—	2	1	no	—
589	C₂×C₄²	—	2	1	no	—
590	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
591	#107	—	2	2	no	—
592	#103	—	2	2	no	—
593	#103	—	2	2	no	—
594	#103	—	2	2	no	—
595	#103	—	2	2	no	—
596	#103	—	2	2	no	—
597	#103	—	2	2	no	—
598	#103	—	2	2	no	—
599	#103	—	4	1	no	—
600	#103	D₄×C₇₉	1	4	yes	complemented
601	#102	—	2	2	no	—
602	C₂²⋊C₈	—	2	2	no	—
603	C₂²⋊C₈	—	2	2	no	—
604	C₂²⋊C₈	—	4	1	no	—
605	#95	—	2	1	no	—
606	#95	—	2	1	no	—
607	C₂⁴	—	2	1	no	—
608	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
609	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
610	C₂×Q₈	—	2	4	no	—
611	C₂×Q₈	—	2	4	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	8	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	4	2	no	—
627	C₂×Q₈	—	4	2	no	—
628	C₂×Q₈	—	4	2	no	—
629	C₂×Q₈	—	4	2	no	—
630	C₂×Q₈	—	4	4	no	—
631	C₂×Q₈	—	4	4	no	—
632	C₂×Q₈	—	4	4	no	—
633	C₂×Q₈	—	4	4	no	—
634	C₂×Q₈	—	4	4	no	—
635	C₂×Q₈	—	4	4	no	—
636	C₂×Q₈	—	4	4	no	—
637	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
638	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
639	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
640	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
641	C₂×Q₈	#41×C₇₉	1	2	yes	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	4	2	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	8	1	no	—
655	C₂×D₄	—	8	1	no	—
656	C₂×D₄	—	8	1	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
683	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
684	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
685	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
687	SD₁₆	—	4	4	no	—
688	SD₁₆	—	4	4	no	—
689	SD₁₆	—	4	4	no	—
690	M₁₆	—	4	4	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	2	1	no	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	2	1	no	—
695	C₂×C₈	—	2	1	no	—
696	C₂×C₈	—	2	1	no	—
697	C₂×C₈	—	2	1	no	—
698	C₂×C₈	—	2	1	no	—
699	C₂×C₈	—	2	1	no	—
700	C₂×C₈	—	2	1	no	—
701	C₂×C₈	—	2	1	no	—
702	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	8	1	no	—
716	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
717	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	—	8	1	no	—
727	C₂²⋊C₄	—	8	1	no	—
728	C₄²	—	2	4	no	—
729	C₄²	—	2	1	no	—
730	C₄²	—	2	1	no	—
731	C₄²	—	4	2	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	2	1	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	1	no	—
741	C₂³	—	2	1	no	—
742	C₂³	—	2	1	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	1	no	—
748	C₂³	—	4	1	no	—
749	C₂³	—	4	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	#120×C₇₉	1	2	yes	—
752	C₂³	#137×C₇₉	1	2	yes	—
753	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
754	Q₈	—	2	2	no	—
755	Q₈	—	2	2	no	—
756	Q₈	—	2	2	no	—
757	Q₈	—	2	2	no	—
758	Q₈	—	2	2	no	—
759	Q₈	—	2	2	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	4	8	no	—
762	Q₈	—	4	8	no	—
763	Q₈	—	4	1	no	—
764	Q₈	—	4	1	no	—
765	Q₈	—	4	1	no	—
766	Q₈	—	4	1	no	—
767	Q₈	#121×C₇₉	1	4	yes	—
768	D₄	—	2	8	no	—
769	D₄	—	4	1	no	—
770	D₄	—	4	1	no	—
771	D₄	—	4	1	no	—
772	D₄	—	4	1	no	—
773	D₄	—	8	4	no	—
774	D₄	—	8	4	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	8	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	#120×C₇₉	1	2	yes	—
817	C₂×C₄	#137×C₇₉	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
819	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
820	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
821	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
822	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
823	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
824	C₈	—	2	2	no	—
825	C₈	—	4	1	no	—
826	C₈	—	4	1	no	—
827	C₈	—	4	1	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	8	1	no	—
843	C₂²	—	8	1	no	—
844	C₂²	—	8	1	no	—
845	C₂²	—	8	1	no	—
846	C₂²	—	8	1	no	—
847	C₂²	—	8	1	no	—
848	C₂²	—	8	1	no	—
849	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
850	C₂²	D₄²×C₇₉	1	1	yes	characteristic
851	C₂²	#546×C₇₉	1	1	yes	characteristic
852	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
853	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
854	C₂²	#577×C₇₉	1	1	yes	characteristic
855	C₂²	#577×C₇₉	1	1	yes	characteristic
856	C₄	—	2	2	no	—
857	C₄	—	2	4	no	—
858	C₄	—	2	2	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	8	1	no	—
866	C₄	—	8	1	no	—
867	C₄	C₂×#121×C₇₉	1	1	yes	characteristic
868	C₄	#534×C₇₉	1	1	yes	characteristic
869	C₄	D₄²×C₇₉	1	1	yes	characteristic
870	C₄	#546×C₇₉	1	1	yes	characteristic
871	C₂	—	4	2	no	—
872	C₂	—	4	2	no	—
873	C₂	—	16	1	no	—
874	C₂	C₇₉×#2410	1	1	yes	characteristic
875	C₂	C₇₉×#3004	1	1	yes	characteristic
876	C₂	C₇₉×#3010	1	1	yes	characteristic
877	C₂	C₇₉×#3266	1	1	yes	characteristic
878	C₂	C₇₉×#3278	1	1	yes	characteristic
879	C₂	C₇₉×#3320	1	1	yes	characteristic
880	C₂	C₇₉×#3329	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₇₉×#2414	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×C₄×D₄×C₇₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×D₄×Q₈×C₇₉	C₂	semidirect
2. C₂×#468×C₇₉	C₂	semidirect
3. C₂×#448×C₇₉	C₂	semidirect
4. C₂×#448×C₇₉	C₂	semidirect
5. C₂×#419×C₇₉	C₂	semidirect
7. C₇₉×#2043	C₂	semidirect
8. C₇₉×#2036	C₂	semidirect
9. C₇₉×#2013	C₂	semidirect
10. C₇₉×#2000	C₂	semidirect
11. C₇₉×#1880	C₂	semidirect
12. C₇₉×#1873	C₂	semidirect
13. C₇₉×#1870	C₂	semidirect
14. C₇₉×#1863	C₂	semidirect
15. C₇₉×#1787	C₂	semidirect
78. C₂²×Q₈×C₇₉	D₄	semidirect
114. C₂²⋊Q₈×C₇₉	D₄	semidirect
159. #103×C₇₉	D₄	semidirect
430. #24445	C₇₉	direct (N × H)
441. C₂×D₄×Q₈	C₂×C₇₉	semidirect
442. C₂×#468	C₂×C₇₉	semidirect
443. C₂×#448	C₂×C₇₉	semidirect
444. C₂×#448	C₂×C₇₉	semidirect
445. C₂×#419	C₂×C₇₉	semidirect
447. #2043	C₂×C₇₉	semidirect
448. #2036	C₂×C₇₉	semidirect
449. #2013	C₂×C₇₉	semidirect
450. #2000	C₂×C₇₉	semidirect
451. #1880	C₂×C₇₉	semidirect
452. #1873	C₂×C₇₉	semidirect
453. #1870	C₂×C₇₉	semidirect
454. #1863	C₂×C₇₉	semidirect
455. #1787	C₂×C₇₉	semidirect
456. C₇₉	#24445	direct (N × H)
519. C₂²×Q₈	D₄×C₇₉	semidirect
555. C₂²⋊Q₈	D₄×C₇₉	semidirect
600. #103	D₄×C₇₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₄×Q₈×C₇₉	2
C₂×#468×C₇₉	2
C₂×#448×C₇₉	2
C₂×#419×C₇₉	2
C₇₉×#2414	2
C₇₉×#2043	2
C₇₉×#2036	2
C₇₉×#2013	2
C₇₉×#2000	2
C₇₉×#1880	2
C₇₉×#1873	2
C₇₉×#1870	2
C₇₉×#1863	2
C₇₉×#1787	2
#24445	79

Subgroups — C79×#24445 #34136134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24445 #34136134